Adiabatic Quantum Computation Research Articles

Quantum software engineering. Pt. I: Quantum Circuit (Gate) Model based Computing – education Lectures and pedagogical workshop

All the quantum algorithms are based on a certain quantum computing model, varying from the quantum circuit, one-way quantum computation, adiabatic quantum computation and topological quantum computation. These four models are equivalent in computational power; among them, the quantum circuit model is most frequently used. In the circuit model, it has been proved that arbitrary single-qubit rotations plus twoqubit controlled-NOT gates are universal, i.e. they can provide a set of gates to implement any quantum algorithm. This article discusses the goal for this research: it is to given a lightning-fast (as-barebones-as-possible) definition of the quantum circuit model computing and leisurely development of quantum computation before actually getting around to sophisticated algorithms. In this article the main ideas of quantum software engineering is described.

De-Signing Hamiltonians for Quantum Adiabatic Optimization

Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We introduce a transformation that maps every non-stoquastic adiabatic path ending in a classical Hamiltonian to a corresponding stoquastic adiabatic path by appropriately adjusting the phase of each matrix entry in the computational basis. We compare the spectral gaps of these adiabatic paths and find both theoretically and numerically that the paths based on non-stoquastic Hamiltonians have generically smaller spectral gaps between the ground and first excited states, suggesting they are less useful than stoquastic Hamiltonians for quantum adiabatic optimization. These results apply to any adiabatic algorithm which interpolates to a final Hamiltonian that is diagonal in the computational basis.

Universal computation with quantum fields

We explore a way of universal quantum computation with particles which cannot occupy the same position simultaneously and are symmetric under exchange of particle labels. Therefore the associated creation and annihilation operators are neither bosonic nor fermionic. In this work we first show universality of our method and numerically address several examples. We demonstrate dynamics of a Bloch electron system from a viewpoint of adiabatic quantum computation. In addition we provide a novel Majorana fermion system and analyze phase transitions with spin-coherent states and the time average of the out-of-time-order correlator (OTOC). We report that a first-order phase transition is avoided when it evolves in a non-stoquastic manner and the time average of the OTOC diagnoses the phase transitions successfully.

Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory

Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo simulation, consequently it usually suffers such problems as the Fermion sign problem and the lack of real-time dynamics. Hopefully they can be avoided by using quantum simulation, which simulates quantum systems by using controllable true quantum processes. The field of quantum simulation is under rapid development. Here we present a circuit-based digital scheme of quantum simulation of quantum ℤ2 lattice gauge theory in 2 + 1 and 3 + 1 dimensions, using quantum adiabatic algorithms implemented in terms of universal quantum gates. Our algorithm generalizes the Trotter and symmetric decompositions to the case that the Hamiltonian varies at each step in the decomposition. Furthermore, we carry through a complete demonstration of this scheme in classical GPU simulator, and obtain key features of quantum ℤ2 lattice gauge theory, including quantum phase transitions, topological properties, gauge invariance and duality. Hereby dubbed pseudoquantum simulation, classical demonstration of quantum simulation in state-of-art fast computers not only facilitates the development of schemes and algorithms of real quantum simulation, but also represents a new approach of practical computation.

Efficient diabatic quantum algorithm in number factorization

Adiabatic quantum algorithm is developed to reduce the time complexity of a classical nondeterministic polynomial problem to a polynomial one. However, our numerical and analytical results reveal that the evolution time of the factorization with a standard adiabatic quantum algorithm increases exponentially with the system size. By introducing the expectation of practical computation time TE, we find the optimal TE on the single evolution time requires the quantum algorithm to work in the diabatic regime, contrast to the traditional adiabatic quantum algorithm.

Optimizing adiabatic quantum pathways via a learning algorithm

Designing proper time-dependent control fields for slowly varying the system to the ground state that encodes the problem solution is crucial for adiabatic quantum computation. However, inevitable perturbations in real applications demand us to accelerate the evolution so that the adiabatic errors can be prevented from accumulation. Here, by treating this trade-off task as a multiobjective optimization problem, we propose a gradient-free learning algorithm with pulse smoothing technique to search optimal adiabatic quantum pathways and apply it to the Landau-Zener Hamiltonian and Grover search Hamiltonian. Numerical comparisons with a linear schedule, local adiabatic theorem induced schedule, and gradient-based algorithm searched schedule reveal that the proposed method can achieve significant performance improvements in terms of the adiabatic time and the instantaneous ground-state population maintenance. The proposed method can be used to solve more complex and real adiabatic quantum computation problems.

Performance evaluation of adiabatic quantum computation via quantum speed limits and possible applications to many-body systems

The quantum speed limit specifies a universal bound of the fidelity between the initial state and the time-evolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the time-evolved state. The bound is characterized by the counterdiabatic Hamiltonian and can be used to evaluate the worst case performance of the adiabatic quantum computation. The result is improved by imposing additional conditions and we examine several models to find a tight bound. We also derive a different type of quantum speed limits that is meaningful even when we take the thermodynamic limit. By using solvable spin models, we study how the performance and the bound are affected by phase transitions.

Quantum adiabatic algorithm design using reinforcement learning

Quantum algorithm design plays a crucial role in exploiting the computational advantage of quantum devices. Here we develop a deep-reinforcement-learning based approach for quantum adiabatic algorithm design. Our approach is generically applicable to a class of problems with solution hard-to-find but easy-to-verify, e.g., searching and NP-complete problems. We benchmark this approach in Grover-search and 3-SAT problems, and find that the adiabatic-algorithm obtained by our RL approach leads to significant improvement in the resultant success probability. In application to Grover search, our RL-design automatically produces an adiabatic quantum algorithm that has the quadratic speedup. We find for all our studied cases that quantitatively the RL-designed algorithm has a better performance compared to the analytically constructed non-linear Hamiltonian path when the encoding Hamiltonian is solvable, and that this RL-design approach remains applicable even when the non-linear Hamiltonian path is not analytically available. In 3-SAT, we find RL-design has fascinating transferability---the adiabatic algorithm obtained by training on a specific choice of clause number leads to better performance consistently over the linear algorithm on different clause numbers. These findings suggest the applicability of reinforcement learning for automated quantum adiabatic algorithm design. Further considering the established complexity-equivalence of circuit and adiabatic quantum algorithms, we expect the RL-designed adiabatic algorithm to inspire novel circuit algorithms as well. Our approach is potentially applicable to different quantum hardwares from trapped-ions and optical-lattices to superconducting-qubit devices.

Iterative classical superadiabatic algorithm for combinatorial optimization

We consider a classical and superadiabatic version of an iterative quantum adiabatic algorithm to solve combinatorial optimization problems. This algorithm is deterministic because it is based on purely classical dynamics, that is, it does not rely on any stochastic approach to mimic quantum dynamics. Moreover, we use the exact shortcut to adiabaticity for stationary states of classical spin systems, and thus the final state of an annealing process does not depend on the annealing time. We apply this algorithm to a certain class of hard instances of the 3-SAT problem, which is specially hard for purely adiabatic algorithms. We find that more than 90% of such 64-bits hard instances, which we try to solve, can be resolved by a few iteration. Our approach can also be used to analyze properties of instances themselves apart from stochastic uncertainty and shortage of adiabaticity.

Error-run-time trade-off in the adiabatic approximation beyond scaling relations

The use of the adiabatic approximation in practical applications, as in adiabatic quantum computation, demands an assessment of the errors made in finite-time evolutions. Aiming at such scenarios, we derive bounds relating error and evolution time in the adiabatic approximation that go beyond typical scaling relations. Using the Adiabatic Perturbation Theory, we obtain leading-order expressions valid for long evolution time T, while explicitly determining the shortest time T and the largest error ε for which they are valid. In this validity regime, we can make clear and precise statements about the evolution time needed to reach a given error and vice-versa. As an example of practical importance, we apply these results to the adiabatic search, and obtain for the first time an error-run-time trade-off relation that fully reproduces the discrete-Grover-search scaling. We also pioneer the obtention of tight numerical values for ε and T under the error-reducing strategy “boundary cancelation”.

Simulating quantum circuits by adiabatic computation: Improved spectral gap bounds

Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a mapping of a quantum circuit to an an adiabatic evolution, and then showing that the minimum spectral gap of the adiabatic Hamiltonian is at least inverse polynomial in the number of computational steps $L$. In this paper we provide two simplified proofs that the gap is inverse polynomial. Both proofs result in the same lower bound for the minimum gap, which for $L \gg 1$ is $\min_s\Delta \gtrsim \pi^2 / [8(L+1)^2]$, an improvement over previous estimates. Our first method is a direct approach based on an eigenstate ansatz, while the the second uses Weyl's theorem to leverage known exact results into a bound for the gap. Our results suggest that it may be possible to use these methods to find bounds for spectral gaps of Hamiltonians in other scenarios.

Using the Energy Distribution as a Benchmarking Among Models for Adiabatic Quantum Processing in the Protein Folding Problem

Determining the tertiary complexity of proteins using ab-initio algorithms is a hard problem. Adiabatic Quantum Computing allows to construct simple Ising-like Hamiltonians in order to elucidate the aminoacid interactions minimizing the conformation energy of the protein. Exploring the energy distribution of the Hamiltonian allows to compare the efficiency of different models there proposed. This article compare the efficiency of two algorithms through the conformation energy of a protein stating a benchmark through the energy distributions of the conformation states.

Demonstration of a Nonstoquastic Hamiltonian in Coupled Superconducting Flux Qubits

Hamiltonian-based quantum computation is a class of quantum algorithms in which the problem is encoded in a Hamiltonian and the evolution is performed by a continuous transformation of the Hamiltonian. Universal adiabatic quantum computing, quantum simulation, and quantum annealing are examples of such algorithms. Up to now, all implementations of this approach have been limited to qubits coupled via a single degree of freedom. This gives rise to a stoquastic Hamiltonian that has no sign problem in quantum Monte Carlo simulations. In this paper, we report implementation and measurements of two superconducting flux qubits coupled via two canonically conjugate degrees of freedom—charge and flux—to achieve a nonstoquastic Hamiltonian. We perform microwave spectroscopy to extract circuit parameters and show that the charge coupling manifests itself as a σyσy interaction in the computational basis. We observe destructive interference in quantum coherent oscillations between the computational-basis states of the two-qubit system. Finally, we show that the extracted Hamiltonian is nonstoquastic over a wide range of parameters.5 MoreReceived 8 November 2019Revised 9 January 2020Accepted 18 February 2020DOI:https://doi.org/10.1103/PhysRevApplied.13.034037© 2020 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasQuantum coherence & coherence measuresQuantum computationQuantum information with solid state qubitsQuantum stochastic processesPhysical SystemsCoupled oscillatorsSuperconducting qubitsTechniquesQuantum Monte CarloSimulated annealingQuantum InformationCondensed Matter, Materials & Applied Physics

Theory versus practice in annealing-based quantum computing

This paper introduces basic concepts of annealing-based quantum computing, also known as adiabatic quantum computing (AQC) and quantum annealing (QA), and surveys what is known about this novel computing paradigm. Extensive empirical research on physical quantum annealing processers built by D-Wave Systems has exposed many interesting features and properties. However, because of longstanding differences between abstract and empirical approaches to the study of computational performance, much of this work may not be considered relevant to questions of interest to complexity theory; by the same token, several theoretical results in quantum computing may be considered irrelevant to practical experience.To address this communication gap, this paper proposes models of computation and of algorithms that lie on a scale of instantiation between pencil-and-paper abstraction and physical device. Models at intermediate points on these scales can provide a common language, allowing researchers from both ends to communicate and share their results. The paper also gives several examples of common terms that have different technical meanings in different regions of this highly multidisciplinary field, which can create barriers to effective communication across disciplines.

Simulated Bifurcation Algorithm Inspired by Adiabatic Quantum Computation

Simulated Bifurcation Algorithm Inspired by Adiabatic Quantum Computation

Vacancies in graphene: an application of adiabatic quantum optimization.

Quantum annealers have grown in complexity to the point that quantum computations involving a few thousand qubits are now possible. In this paper, with the intentions to show the feasibility of quantum annealing to tackle problems of physical relevance, we used a simple model, compatible with the capability of current quantum annealers, to study the relative stability of graphene vacancy defects. By mapping the crucial interactions that dominate carbon-vacancy interchange onto a quadratic unconstrained binary optimization problem, our approach exploits the ground state as well as the excited states found by the quantum annealer to extract all the possible arrangements of multiple defects on the graphene sheet together with their relative formation energies. This approach reproduces known results and provides a stepping stone towards applications of quantum annealing to problems of physical-chemical interest.

Quantum adiabatic algorithms using unitary interpolation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504430, 11805279, 61501514, and 61502526).

We present two efficient quantum adiabatic algorithms for Bernstein–Vazirani problem and Simon’s problem. We show that the time complexities of the algorithms for Bernstein–Vazirani problem and Simon’s problem are O(1) and O(n), respectively, which are the same complexities as the corresponding algorithms in quantum circuit model. In these two algorithms, the adiabatic Hamiltonians are realized by unitary interpolation instead of standard linear interpolation. Comparing with the adiabatic algorithms using linear interpolation, the energy gaps of our algorithms keep constant. Therefore, the complexities are much easier to analyze using this method.

Quantum Computing with Octonions

There are two schools of "measurement-only quantum computation". The first ([11]) using prepared entanglement (cluster states) and the second ([4]) using collections of anyons, which according to how they were produced, also have an entanglement pattern. We abstract the common principle behind both approaches and find the notion of a graph or even continuous family of equiangular projections. This notion is the leading character in the paper. The largest continuous family, in a sense made precise in Corollary 4.2, is associated with the octonions and this example leads to a universal computational scheme. Adiabatic quantum computation also fits into this rubric as a limiting case: nearby projections are nearly equiangular, so as a gapped ground state space is slowly varied the corrections to unitarity are small.

High-Coherence Fluxonium Qubit

We report superconducting fluxonium qubits with coherence times largely limited by energy relaxation and reproducibly satisfying T2 > 100 microseconds (T2 > 300 microseconds in one device). Moreover, given the state of the art values of the surface loss tangent and the 1/f flux noise amplitude, coherence can be further improved beyond 1 millisecond. Our results violate a common viewpoint that the number of Josephson junctions in a superconducting circuit -- over 100 here -- must be minimized for best qubit coherence. We outline how the unique to fluxonium combination of long coherence time and large anharmonicity can benefit both gate-based and adiabatic quantum computing.

Analog nature of quantum adiabatic unstructured search

The quantum adiabatic unstructured search algorithm is one of only a handful of quantum adiabatic optimization algorithms to exhibit provable speedups over their classical counterparts. With no fault tolerance theorems to guarantee the resilience of such algorithms against errors, understanding the impact of imperfections on their performance is of both scientific and practical significance. We study the robustness of the algorithm against various types of imperfections: limited control over the interpolating schedule, Hamiltonian misspecification, and interactions with a thermal environment. We find that the unstructured search algorithm’s quadratic speedup is generally not robust to the presence of any one of the above non-idealities, and in some cases we find that it imposes unrealistic conditions on how the strength of these noise sources must scale to maintain the quadratic speedup.